A gyroscope clock for a null gravitational redshift experiment

This dissertation describes the analysis and experimental testing of the frequency stability of electrostatically-levitated, superconducting gyroscopes. The tests were conducted on the ground at cryogenic temperatures using a magnetic readout of the gyroscope rotor's spin phase. By achieving fractional frequency stabilities on the order of 3 {dollar}times{dollar} 10{dollar}sp{lcub}-11{rcub}{dollar} (or better) over one year it would be possible to perform a test of Local Position Invariance (LPI) to the 10% level. LPI states that in local freely falling frames, the outcome of any non-gravitational test is independent of where and when in the universe it is performed. This means that all clocks, independent of the physical principle on which they are based, should exhibit the same gravitational redshift. The experiment proposed in this thesis is intended to compare a gyroscope clock to an atomic clock as they both experience the same time-varying gravitational potential. Since there is expected to be no difference between the two types of clocks, this is a null gravitational redshift experiment.; A unique opportunity to perform a gravitational redshift experiment exists in the Gravity Probe B (GPB) program. GPB is a satellite experiment whose purpose is to test two predictions of Einstein's General Theory of Relativity: the geodetic and frame-dragging effects. These effects will be measured by monitoring the precession rates of nearly perfect gyroscopes against the inertial stars. Navigation of the satellite is aided by means of the Global Positioning System (GPS). Thus GPB already has in place nearly all of the essential elements for the proposed clock experiment. These include nearly disturbance-free gyroscopes whose pointing and spin phase can be referenced to the inertial frame of the fixed stars and onboard access to Earth-bound atomic clocks through GPS. The varying gravitational potential is provided by the eccentricity of the Earth's orbit about the Sun. Therefore with very little change to GPB, the clock experiment can be performed using the same gyroscopes. I have performed extensive ground-based testing which indicates that it should be possible to achieve a spin frequency stability of 3 {dollar}times{dollar} 10{dollar}sp{lcub}-12{rcub}{dollar} or better in space.